But the Chinese carrier would definitely complicate things if they got it operational.
I agree with analysis you gave, but cannot underestimate any adversary with the wealth, growing technical and manufacturing expertise, and the enormous number of potential fighters the Chinese have.
Yes using Taiwan as a land shield for our own carriers is a great advantage for our carriers. And definitely, underestimation can REALLY get you killed. That's sure what nailed the krauts and japs to the wall in WWII after we came in, and before really. They did so many audacious things so certain that we were weak and wouldn't or couldn't stand up to them. Then reality knocked them down. The Chinese carrier/s should be treated as a serious threat that can defeat a powerful Nimitz carrier task force, even if it's known that it would be defeated before sinking any of our ships. It's still a good idea to treat it as though it could beat you to stop any complacency before it happens.
I would add "WILL" to your list. They have the will and would not bat an eye at losing a few million of their own people. Our fifth column within would start crying for surrender before we lost even a thousand.